Henry was part of the last Arsenal team to win a major trophy - the FA Cup in 2005 - and Wenger has been criticised for the lack of success in recent season.
However, Arsenal have topped the Premier League for much of this season, and are also through to the last 16 of the UEFA Champions League, and Henry says Wenger can prove his critics wrong.
In an exclusive interview with Sky Sports, Henry said: "He has said it himself, when you don't win trophies obviously people are going to talk and obviously people are going to say he's not the man for the job anymore.
"I think Arsene himself understood that. When you don't have something to show at the end of the season it is difficult to talk and to stop all of the critics.
"But this year he is showing everybody that Arsenal can compete again."
Henry also expressed surprise that Wenger smashed the club's transfer record by signing Mesut Ozil from Real Madrid for £40million, but says the German's form so far proves it was a shrewd move.
"The player that he has signed for £40million is just like a great player," he added.
"When you look at him playing when he has the ball it seems like he has all the time in the world - and I can tell you for a fact it's not that easy.
"He paid the price to have a player like Ozil, but I think that right now it's showing that it's worth it and hopefully in the end it will show more."
Meanwhile, Henry says he dreams of returning to Arsenal in some capacity once his playing career ends.
The Frenchman, who is the club's all-time leading goalscorer, is about to enter the final year of his contract with MLS side New York Red Bulls and remains coy over what his future holds.
However, he insists he would relish the chance to go back to Arsenal where he enjoyed eight successful years between 1999 and 2007 and admits the thought of becoming their manager has crossed his mind.
Henry said: "I would love to be around the game and - I've said it so many times - hopefully around Arsenal.
"What am I going to do? I don't know if it's going to be coaching. I really don't know yet. I'm trying to finish my career, which is something I have to concentrate on.
"This is my last year actually, the one coming, on paper. I'm not saying I'm retiring, I'm saying that's my last year on paper to make it clear.
"I don't know [if I'll ever be Arsenal manager]. I'm sure if you asked any Arsenal fan they would love to be the Arsenal manager, but I actually don't know.
"You need to do some stuff before that. You can't pretend that you can come and be a manager. It's really difficult.
"The dream for me would be to be back at Arsenal. The rest we will see, but the dream would be to be back at Arsenal, obviously."
Don't miss a second chance to watch Thierry Henry: The Interview - tonight, Sky Sports 1 at 6.30pm